Looks like a cool restore project. Also looks like the one I currently have in some mannerisms.... http://forums.bicycletutor.com/thread-1201.html . Other then that I really have no info on it, maybe someone else does.
Try to get a close up look on the rear hub of ANY and ALL printed text and numbers. That would help out.

Good maintenance to your Bike, can make it like the wheels are, true and smooth!

You have my bike. That is, you have a duplicate of my bike. I own an identical black Sears, which I picked up at a flea market in Chicago for $60 two years ago, it is identical to yours but for the rust and the back rack. My Shimano rear hub was busted: missing innards, cable, and shifter; my local bike ship couldn't repair the hub but otherwise fixed the whole bike up, I rode it as a single-speed for a season before deciding I was too fat and old to do without gears.

Another local bike shop promised to fix the hub but what they did was swap the entire rear wheel, which came off an earlier Sears bike built by Puch. My 3-speed IGH is now the Sears 501.3 which in turn (I discovered) was an exact copy (except for the shell) of the immortal Sturmey-Archer AW built under license by Steyr in Austria.

So what we each have, so I am told, is a post-1972 (note the BMA sticker) US-built bike, styled after the Puch bikes Sears imported from Austria in the mid-sixties (I have seen them with my hub, with SRAM Torpedo hubs, and as 5-speed derailleur bikes), though that dimple in the front fender is a nod to Raleigh. One shop told me they were built by Bendix, another said C.F. Murray. The decals are identical to the ones on the Puch bikes. Your hub is original, which made me wonder if the bikes were built in Japan or Taiwan, but the BMA sticker belies this.

I have seen one other example of this bike, owned by one of my local barristas. His has the Shimano hub, it's in very good shape, and he loves it.

My bike had a Mesinger saddle which my rump hated, and I have replaced it with a comfort seat, though I had to go to an old-bike-parts specialist to find a bracket to fit the odd truncated post. My tires are Korean, and, I suspect, not original. My brakes have the brand name "SAC" on them, but for all I know that means "Sears Approved Commodity."

The Shimano 333 hub has a poor reputation for longevity in the USA, allegedly they did not stand up to hard use or heavy riders. On the other hand when they work they shift very smoothly and have a slightly wider gear range than the traditional SA -type hub.

I am advised that this frame is heavy but decent, even if it is butt-welded and not lugged, that Sears still stood behind their products in those days and were not coasting on mere tradition of quality. You will have to de-rust the chain, clean out and re-grease the bottom bracket, and possibly get a professional to overhaul your hub (I hear this means taking out the internal cartridge and stuffing it full of grease). It is not as smooth as the 1969 Schwinn I later bought to keep at my girlfriend's house, but I enjoy riding it, and it is unattractive to thieves.

I would like to know, definitively, where our bikes came from, and seek help from the rest of the Web. This was my first bike in 30 years and has grown me up from an ignoramus to an involved bicycle fan.